4.2.2 inductive statistics 1 upa package 4, module 2 inductive statistics

14.2.2 Inductive Statistics

UPA Package 4, Module 2

INDUCTIVE STATISTICS


Inductive Statistics

• Statistics and the Geographic Research Process• Normal Distribution• Inductive Statistics• Correlations and Relationships• Introduction exercise 4.2.2


Statistics and the Geographic Research Process


Frequency Distributions

0 5 10

Household members total

0

50

100

150

200

250

300

Fre

qu

ency

Mean = 5.16Std. Dev. = 2.319N = 1,510

Histogram

0.00 20000.00 40000.00 60000.00 80000.00 100000.00120000.00

Total Wage Income 2002

0

100

200

300

400

500

Fre

qu

ency

Mean = 6951.0865Std. Dev. = 9423.36206N = 855


Normal Distribution

• Normal curve• Bell-shape curves described by its mean (center of the

distribution) and standard deviation (shape of the curve)


Normal Distribution

• Areas under the normal curve• The 68 – 95 - 99.7% rule

• Z or standard scores

• Standard score =


Normal Distribution

• Symmetrical distributions • Positive and negatively

skewed distributions • Mean not equal to median• Impact of extreme cases

e.g. very high incomes on mean



• Hypotheses

Null and Research Hypothesis

Assumptions• Level of significance

Two and one tailed test

Degree of Freedom• Tests

Parametric and non-parametric tests• Cross tables



Income

20000180001600014000120001000080006000

Hou

se v

alue

200

180

160

140

120

100

80

60

40

20

scattergram (house value / income)



• Tests• Level of significance• Cross tablesEA Slum Type * Slum/Non-Slum Cross tabulation

Slum/Non-Slum

Slum

households Non-slum

households Total

Count 548260 82700 630960 Slum % of Total 26.8% 4.0% 30.9% Count 252340 1161180 1413520

EA Slum Type

Non-slum % of Total 12.3% 56.8% 69.1% Count 800600 1243880 2044480 Total % of Total 39.2% 60.8% 100.0%



Procedure for testing statistical hypotheses:• Assumptions• Sampling procedure• Sign. Level, critical region• Testing• Decision/conclusions


Correlations and Relationships

Correlations

House Value Income House Value 1.000 .815 Pearson Correlation

Income .815 1.000

HOUSES_$ . .000 Sig. (1-tailed)

TTLRES_$ .000 .

HOUSES_$ 87 87 N

TTLRES_$ 87 87

Correlation Coefficient 0.815


Introduction Exercise 4.2.2

• Create Histograms• visual check on normality• Calculate z-scores and ‘areas under the normal curve’• Create a scattergram• Calculate correlation coefficient


Introduction Exercise 4.2.2

Histogram / Bar chart

Earth/Sand/Mud

Mud m

ixed with dung

Coarse wood planks

Palm/bam

boo

Cement (not polished)

Parquet or polished wood

Linoleum

Ceramic tiles

Cement (polished)

Carpet

Terrazzo

0

100

200

300

400

500

600

Fre

qu

ency

What is the most common material of the floor in the living room?

0 10000 20000 30000

Income

0

500

1,000

1,500

Fre

qu

ency

Mean = 10027.12Std. Dev. = 1974.064N = 8,976

Median=9756.00


Introduction to Exercise 4.2.2

Population density vs. Income

Data refer to mean values per municipality in the Netherlands

Higher Income – higher population densities?

8000 10000 12000 14000

income

0

2000

4000

6000

8000

10000

12000

po

p_d

n_1

R Sq Linear = 0.087

4.2.2 inductive statistics 1 upa package 4, module 2 inductive statistics

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